Correlation to the Common Core State Standards for Mathematics Algebra 2 Houghton Mifflin Harcourt Algerbra 2 2015
Houghton Mifflin Harcourt Algebra II 2015 correlated to the Common Core State Standards for Mathematics Algebra II Standards for Mathematical Practice SMP.1 Make sense of problems and persevere in solving them. Integrated throughout the book. Examples: SE: 14 16, 30, 38 40, 46, 60, 62, 69 70, 990, 1057 SMP.2 Reason abstractly and quantitatively. Integrated throughout the book. Examples: SE: 10-11, 28 29, 30, 51, 56, 85, 124, 137, 173, 188 SMP.3 Construct viable arguments and critique the reasoning of others. Integrated throughout the book. Examples: SE: 14, 29, 84, 125, 137, 151, 247, 417, 555 SMP.4 Model with mathematics. Integrated throughout the book. Examples: SE: 10 11, 20 22, 38 40, 50 52, 69-70, 126, 255-257, 391-392 SMP.5 Use appropriate tools strategically. Integrated throughout the book. Examples: SE: 20 21, 210 212, 249 264, 299 300, 361, 408 410, 1138, 1200 SMP.6 Attend to precision. Integrated throughout the book. Examples: SE: 91 92, 253, 382, 708 709, 960, 1093, 1164 1167 SMP.7 Look for and make use of structure. Integrated throughout the book. Examples: SE: 30, 31 35, 235 236, 297 298, 311 312, 583 584, 597 599, 609, 850 SMP.8 Look for and express regularity in repeated reasoning. Integrated throughout the book. Examples: SE: 127 128, 283 284, 297 301, 311 312, 583 584, 597 599 1
Standards for Mathematical Content N-CN The Complex Number System Perform arithmetic operations with complex numbers. N-CN.A.1 Know there is a complex number i such that i 2 = 1, and every complex number has the form a + bi with a and b real. SE: 113 136, 127 138 N-CN.A.2 Use the relation i 2 = 1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. SE: 127 138, 139 152 Use complex numbers in polynomial identities and equations. N-CN.C.7 Solve quadratic equations with real coefficients that have complex solutions. SE: 139 152 N-CN.C.8 (+) Extend polynomial identities to the complex numbers. SE: 309 320 N-CN.C.9 (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. SE: 353 368 A-SSE Seeing Structure in Expressions Interpret the structure of expressions A-SSE.A.1 Interpret expressions that represent a quantity in terms of its context. SE: 249 264, 309 320, 401 418 A-SSE.A.1a A-SSE.A.1b A-SSE.A.2 Interpret parts of an expression, such as terms, factors, and coefficients. Interpret complicated expressions by viewing one or more of their parts as a single entity. Use the structure of an expression to identify ways to rewrite it. SE: 249 264, 309 320 SE: 401 418 SE: 127 138, 425 438 2
Write expressions in equivalent forms to solve problems A-SSE.B4 Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. SE: 613-628 A-APR Arithmetic with polynomials and rational expressions Perform arithmetic operations on polynomials. A-APR.A.1 Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. Understand the relationship between zeros and factors of polynomials. A-APR.B.2 Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x a is p(a), so p(a) = 0 if and only if (x a) is a factor of p(x). SE: 271 282, 283 296, 297 308, 321 334 SE: 341 352, 353 368 A-APR.B.3 Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. SE: 249 264, 127 138, 321 334, 341 352, 353 368 Use polynomial identities to solve problems A-APR.C.4 Prove polynomial identities and use them to describe numerical relationships. Rewrite rational expressions A-APR.D.6 Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system. SE: 283 296 SE: 321 334, 381 400, 401 418 3
A-APR.D.7 (+) Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions. SE: 425 438, 439 452 A-CED Creating Equations Create equations that describe numbers of relationships A-CED.A.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. SE: 77 86, 87 100, 127 138, 453 466, 557 570 A-CED.A.2 A-CED.A.3 A-CED.A.4 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. SE: 5 16, 17 30, 31 46, 65 76, 159 174, 175 188, 923 936 SE: 5 16, 159 174, 175 188, 203 222, 341 352, 453 466 SE: 425 438, 439 452, 783 798 4
A-REI Reasoning with Equations and Inequalities Understand solving equations as a process of reasoning and explain the reasoning A-REI.A.2 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. SE: 453 466, 557 570 Represent and solve equations and inequalities graphically A-REI.D.11 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. F-IF Interpreting Functions Interpret functions that arise in applications in terms of the context. F-IF.B.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. SE: 77 86, 353 368, 923 936 SE: 17 30, 65 76, 249 264, 495 512, 513 526, 871 888, 889 904, 905 922, 923 936 F-IF.B.5 F-IF.B.6 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. SE: 5 16 SE: 17 30, 495 512, 513 526 5
Analyze functions using different representations. F-IF.C.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. SE: 31 46, 65 76, 87 100, 235 248, 249 264, 353 368, 495 512, 513 526, 543 556, 799 812, 871 888, 889 904, 905 922 F-IF.C.7b F-IF.C.7c F-IF.C.7e F-IF.C.8 F-IF.C.9 Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). SE: 31 46, 65 76, 87 100, 495 512, 513 526, 543 556 SE: 235 248, 249 264, 353 368 SE: 799 812, 871 888, 889 904, 905 922 SE: 271 282, 381 400, 401 418, 439 452, 583 596, 597 612, 667 680, 681 696 SE: 889 904, 905 922 F-BF Building Functions Build a function that models a relationship between two quantities. F-BF.A.1 Write a function that describes a relationship between two SE: 271 282, 283 296, 381 400, 401 418, 439 452, 583 quantities. 596, 597 612, 681 696 F-BF.A.1b Combine standard function types using arithmetic operations. SE: 271 282, 283 296, 381 400, 401 418, 439 452 6
Build new functions from existing functions F-BF.B.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. SE: 31 46, 65 76, 235 248, 381 400, 495 512, 513 526, 871 888, 889 904, 905 922 F-BF.B.4 Find inverse functions. SE: 47 58, 479 494 F-BF.B.4a Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. SE: 479 494 F-LE Linear, Quadratic, and Exponential Models Construct and compare linear, quadratic and exponential models and solve problems F-LE.A.4 For exponential models, express as a logarithm the solution to ab ct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology. SE: 799 812 F-TF Trigonometric Functions Extend the domain of trigonometric functions using the unit circle. F-TF.A.1 Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. SE: 825 838 F-TF.A.2 Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. SE: 839 852 Model periodic phenomena with trigonometric functions F-TF.B.5 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline. SE: 923 936 7
Prove and apply trigonometric identities F-TF.C.8 Prove the Pythagorean identity sin 2 (θ) + cos 2 (θ) = 1 and use SE: 853 864 it to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle. S-ID Interpreting Categorical and Quantitative Data Summarize, represent, and interpret data on a single count or measurement variable S-ID.A.4 Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve. SE: 1095 1110, 1131 1140 S-IC Making Inferences and Justifying Conclusions Understand and evaluate random processes underlying statistical experiments. S-IC.A.1 Understand statistics as a process for making inferences about population parameters based on a random sample from that population SE: 1083 1094 S-IC.A.2 Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. SE: 117 1130 Make inferences and justify conclusions from sample surveys, experiments, and observational studies. S-IC.B.3 Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. SE: 1179 1192 S-IC.B.4 S-IC.B.5 Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. SE: 1141 1156, 1163 1178 SE: 1193 1210 S-IC.B.6 Evaluate reports based on data. SE: 1179 1192 8
S-MD Using Probability to Make Decisions Use probability to evaluate outcomes of decisions. S-MD.B.6 (+) Use probabilities to make fair decisions (e.g., drawing SE: 1049 1058 by lots, using a random number generator). S-MD.B.7 (+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). SE: 1059 1070 9